论文标题
Beurling-tourier代数和复杂化
Beurling-Fourier Algebras and Complexification
论文作者
论文摘要
在本文中，我们开发了一种新方法，该方法允许识别加权傅立叶代数的Gelfand光谱，作为对相应组和权重类别的相应组的抽象复合物的一个子集。这概括了Ghandehari-Lee-Ludwig-spronk-Turowska（Adv。Math。2021）的最新结果，这些结果涉及某些LIE群体上的Beurling-Fourier代数范围。在离散组的情况下，我们表明beurling-tourier代数的频谱同构为$ g $。
In this paper, we develop a new approach that allows to identify the Gelfand spectrum of weighted Fourier algebras as a subset of an abstract complexification of the corresponding group for a wide class of groups and weights. This generalizes recent related results of Ghandehari-Lee-Ludwig-Spronk-Turowska (Adv. Math. 2021) about the spectrum of Beurling-Fourier algebras on some Lie groups. In the case of discrete groups we show that the spectrum of Beurling-Fourier algebra is homeomorphic to $G$.
